Scaling-correspondence mechanism

In 1970s, Wilson shown the deep connection of renormalization and scaling of the effective Lagrangian. Polchinski further proved that such connection implied renormalizability of perturbative field theory. We develop the mechanism by an extension of scaling transformation of the effective Lagrangian

• introducing a field-map between the quantum fields of the low-energy effective field theory (EFT) and its’ scaling-corresponding (bare) model. We study the mechanism through real scalar ${\varphi }^4$ model. We found if there is a self-interaction of order $N$ from the EFT’s potential, there are (at most) $N-1$ scaling-corresponding models for the same symmetry group of the EFT. We then study the potential application for cosmology by applying the mechanism to inflation paradigm. We found the generated inflation model (from the real scalar ${\varphi }^4$ EFT) is the power-law inflation model. We briefly check the consistency of the generated inflation model against the inflation’s typical observational constraints - spectral index ($n_s$), e-folds, and tensor/scalar ratio ($r$).